Carseats R Notebook
Introduction
Here is my analysis of data/Carseats_org.csv.
Configuration
library(leaps)
library(stringr)
library(caret)
library(ggplot2)
library(DataExplorer)
library(dplyr)
library(ggExtra)
library(RColorBrewer)
library(plotly)
library(corrplot)
library(htmltools)
library(MASS)System Information
Due to the large number of libraries in use I have provided system information.
sessionInfo()R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: macOS High Sierra 10.13.6
Matrix products: default
BLAS: /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib
LAPACK: /anaconda3/lib/R/lib/libRblas.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] MASS_7.3-51.1 htmltools_0.3.6 corrplot_0.84 plotly_4.8.0 RColorBrewer_1.1-2 ggExtra_0.8
[7] dplyr_0.8.0.1 DataExplorer_0.7.0 caret_6.0-81 ggplot2_3.1.0 lattice_0.20-38 stringr_1.4.0
[13] leaps_3.0
loaded via a namespace (and not attached):
[1] Rcpp_1.0.0 lubridate_1.7.4 tidyr_0.8.2 class_7.3-15 assertthat_0.2.0 digest_0.6.18
[7] ipred_0.9-8 foreach_1.4.4 mime_0.6 R6_2.4.0 plyr_1.8.4 stats4_3.5.1
[13] evaluate_0.12 httr_1.4.0 pillar_1.3.1 rlang_0.3.1 lazyeval_0.2.1 rstudioapi_0.9.0
[19] data.table_1.12.0 miniUI_0.1.1.1 rpart_4.1-13 Matrix_1.2-15 rmarkdown_1.11 labeling_0.3
[25] splines_3.5.1 gower_0.1.2 htmlwidgets_1.3 igraph_1.2.4 munsell_0.5.0 shiny_1.2.0
[31] compiler_3.5.1 httpuv_1.4.5.1 xfun_0.4 pkgconfig_2.0.2 base64enc_0.1-3 nnet_7.3-12
[37] tidyselect_0.2.5 tibble_2.0.1 gridExtra_2.3 prodlim_2018.04.18 codetools_0.2-16 viridisLite_0.3.0
[43] later_0.8.0 crayon_1.3.4 withr_2.1.2 recipes_0.1.4 ModelMetrics_1.1.0 grid_3.5.1
[49] xtable_1.8-3 nlme_3.1-137 jsonlite_1.6 gtable_0.2.0 magrittr_1.5 scales_1.0.0
[55] stringi_1.3.1 reshape2_1.4.3 promises_1.0.1 timeDate_3043.102 generics_0.0.2 lava_1.6.5
[61] iterators_1.0.10 tools_3.5.1 glue_1.3.0 purrr_0.2.5 crosstalk_1.0.0 networkD3_0.4
[67] rsconnect_0.8.13 parallel_3.5.1 survival_2.43-3 yaml_2.2.0 colorspace_1.4-0 knitr_1.21 sapply(c('repr', 'IRdisplay', 'IRkernel'), function(p) paste(packageVersion(p))) repr IRdisplay IRkernel
"0.19.2" "0.7.0" "0.8.15" Data
I load the data into r, and drop the “ID” column.
carseats <- read.csv("data/Carseats_org.csv", header = T, stringsAsFactors = T)
drops <- c("X")
carseats <- carseats[ , !(names(carseats) %in% drops)]
head(carseats, 10)Here I create two new data frames to manage numeric and categorical data.
# get vectors of continuous and categorical cols
nums <- dplyr::select_if(carseats, is.numeric)
cats <- dplyr::select_if(carseats, is.factor)
nums[sample(nrow(nums), 10), ]cats[sample(nrow(cats), 10), ]Let’s get some quick summaries of each:
print('Numeric Summaries')[1] "Numeric Summaries"summary(nums) Sales CompPrice Income Advertising Population Price Age
Min. : 0.000 Min. : 77 Min. : 21.00 Min. : 0.000 Min. : 10.0 Min. : 24.0 Min. :25.00
1st Qu.: 5.390 1st Qu.:115 1st Qu.: 42.75 1st Qu.: 0.000 1st Qu.:139.0 1st Qu.:100.0 1st Qu.:39.75
Median : 7.490 Median :125 Median : 69.00 Median : 5.000 Median :272.0 Median :117.0 Median :54.50
Mean : 7.496 Mean :125 Mean : 68.66 Mean : 6.635 Mean :264.8 Mean :115.8 Mean :53.32
3rd Qu.: 9.320 3rd Qu.:135 3rd Qu.: 91.00 3rd Qu.:12.000 3rd Qu.:398.5 3rd Qu.:131.0 3rd Qu.:66.00
Max. :16.270 Max. :175 Max. :120.00 Max. :29.000 Max. :509.0 Max. :191.0 Max. :80.00
Education
Min. :10.0
1st Qu.:12.0
Median :14.0
Mean :13.9
3rd Qu.:16.0
Max. :18.0 print('Categorical Summaries')[1] "Categorical Summaries"summary(cats) ShelveLoc Urban US
Bad : 96 No :118 No :142
Good : 85 Yes:282 Yes:258
Medium:219 str(nums)'data.frame': 400 obs. of 8 variables:
$ Sales : num 9.5 11.22 10.06 7.4 4.15 ...
$ CompPrice : int 138 111 113 117 141 124 115 136 132 132 ...
$ Income : int 73 48 35 100 64 113 105 81 110 113 ...
$ Advertising: int 11 16 10 4 3 13 0 15 0 0 ...
$ Population : int 276 260 269 466 340 501 45 425 108 131 ...
$ Price : int 120 83 80 97 128 72 108 120 124 124 ...
$ Age : int 42 65 59 55 38 78 71 67 76 76 ...
$ Education : int 17 10 12 14 13 16 15 10 10 17 ...str(cats)'data.frame': 400 obs. of 3 variables:
$ ShelveLoc: Factor w/ 3 levels "Bad","Good","Medium": 1 2 3 3 1 1 3 2 3 3 ...
$ Urban : Factor w/ 2 levels "No","Yes": 2 2 2 2 2 1 2 2 1 1 ...
$ US : Factor w/ 2 levels "No","Yes": 2 2 2 2 1 2 1 2 1 2 ...Data Dimensionality
This command is to inspect the different data types in the data.
str(carseats)'data.frame': 400 obs. of 11 variables:
$ Sales : num 9.5 11.22 10.06 7.4 4.15 ...
$ CompPrice : int 138 111 113 117 141 124 115 136 132 132 ...
$ Income : int 73 48 35 100 64 113 105 81 110 113 ...
$ Advertising: int 11 16 10 4 3 13 0 15 0 0 ...
$ Population : int 276 260 269 466 340 501 45 425 108 131 ...
$ Price : int 120 83 80 97 128 72 108 120 124 124 ...
$ ShelveLoc : Factor w/ 3 levels "Bad","Good","Medium": 1 2 3 3 1 1 3 2 3 3 ...
$ Age : int 42 65 59 55 38 78 71 67 76 76 ...
$ Education : int 17 10 12 14 13 16 15 10 10 17 ...
$ Urban : Factor w/ 2 levels "No","Yes": 2 2 2 2 2 1 2 2 1 1 ...
$ US : Factor w/ 2 levels "No","Yes": 2 2 2 2 1 2 1 2 1 2 ...print("")[1] ""print(paste('Number of Columns:', ncol(carseats)))[1] "Number of Columns: 11"print(paste('Number of Numeric Columns:', ncol(nums)))[1] "Number of Numeric Columns: 8"print(paste('Number of Categorical Columns:', ncol(cats)))[1] "Number of Categorical Columns: 3"dim(carseats)[1] 400 11dim(nums)[1] 400 8dim(cats)[1] 400 3Here’s a quick way to examine general properties of the data:
DataExplorer::introduce(data=carseats)Finally, I want to look at the first and last rows of the data set. Just to be safe:
head(carseats, 2)tail(carseats, 2)head(nums, 2)tail(nums, 2)head(cats, 2)tail(cats, 2)Numeric Plotting
I start out with a few general scatter plots.
plot_ly(data=carseats,
x=~Age,
y=~Sales,
mode = 'markers',
type = 'scatter',
color=~ShelveLoc) %>%
layout(title = "Age, Shelf Location, and Sales Scatter Plot", width=900) Specifying width/height in layout() is now deprecated.
Please specify in ggplotly() or plot_ly()This plot below shows good separation and a weak linear trend. These variables are worth investigating.
plot_ly(data=carseats,
x=~Price,
y=~Sales,
mode = 'markers',
type = 'scatter',
color=~ShelveLoc) %>%
layout(title = "Price, Shelf Location, and Sales Scatter Plot", width=900)Specifying width/height in layout() is now deprecated.
Please specify in ggplotly() or plot_ly()Here we inspect the density of the ‘Price vs Sales’ relationship:
plot_ly(data=carseats,
x=~Price,
y=~Sales,
mode = 'markers',
size = ~Price,
type = 'scatter',
colors = "Dark2",
alpha = .6) %>%
layout(title = "Price, US, and Sales Scatter Plot", width=900) Specifying width/height in layout() is now deprecated.
Please specify in ggplotly() or plot_ly()`line.width` does not currently support multiple values.`line.width` does not currently support multiple values.Normalization
I choose to normalize the numeric data in order to be able to plot each variable on the same scale. This will allow me to investigate the variation of each predictor relative to Sales.
preObj <- preProcess(nums, method=c("center", "scale"))
scaled.nums <- predict(preObj, nums)
head(scaled.nums, 2)tail(scaled.nums, 2)str(scaled.nums)'data.frame': 400 obs. of 8 variables:
$ Sales : num 0.7095 1.3185 0.9078 -0.0341 -1.1849 ...
$ CompPrice : num 0.849 -0.911 -0.781 -0.52 1.045 ...
$ Income : num 0.155 -0.738 -1.203 1.12 -0.166 ...
$ Advertising: num 0.656 1.408 0.506 -0.396 -0.547 ...
$ Population : num 0.0757 -0.0328 0.0282 1.3649 0.51 ...
$ Price : num 0.178 -1.385 -1.512 -0.794 0.515 ...
$ Age : num -0.699 0.721 0.35 0.104 -0.946 ...
$ Education : num 1.183 -1.4882 -0.725 0.0382 -0.3434 ...print("")[1] ""summary(scaled.nums) Sales CompPrice Income Advertising Population Price
Min. :-2.65440 Min. :-3.12856 Min. :-1.70290 Min. :-0.9977 Min. :-1.72918 Min. :-3.87702
1st Qu.:-0.74584 1st Qu.:-0.65049 1st Qu.:-0.92573 1st Qu.:-0.9977 1st Qu.:-0.85387 1st Qu.:-0.66711
Median :-0.00224 Median : 0.00163 Median : 0.01224 Median :-0.2459 Median : 0.04858 Median : 0.05089
Mean : 0.00000 Mean : 0.00000 Mean : 0.00000 Mean : 0.0000 Mean : 0.00000 Mean : 0.00000
3rd Qu.: 0.64575 3rd Qu.: 0.65375 3rd Qu.: 0.79834 3rd Qu.: 0.8067 3rd Qu.: 0.90693 3rd Qu.: 0.64219
Max. : 3.10670 Max. : 3.26225 Max. : 1.83458 Max. : 3.3630 Max. : 1.65671 Max. : 3.17633
Age Education
Min. :-1.74827 Min. :-1.48825
1st Qu.:-0.83779 1st Qu.:-0.72504
Median : 0.07268 Median : 0.03816
Mean : 0.00000 Mean : 0.00000
3rd Qu.: 0.78255 3rd Qu.: 0.80137
Max. : 1.64673 Max. : 1.56457 Distributions
Here are scaled distributions (histograms and density plots) for each numeric variable, including Sales. The variables relating to money ($) tend to be approximately normal. Many other variables tend to be approximately uniform, which does not bode well for their predictive power.
scaled.nums %>%
tidyr::gather() %>%
ggplot(aes(x=value,y=..density..))+
ggtitle('Distributions of Continous Variables (scaled)') +
facet_wrap(~ key, scales = "free") +
geom_histogram(fill=I("orange"), col=I("black"), bins = 50) +
facet_wrap(~ key, scales = "free") +
geom_density(color="blue", fill='light blue', alpha = 0.4)
Here we plot all numeric variables against their distributions. This is just another way to examine the information shown above.
scaled.nums %>%
tidyr::gather() %>%
plot_ly(x=~key, y=~value,
type = "box",
boxpoints = "all",
jitter = 0.4,
pointpos = 0,
color = ~key,
colors = "Dark2") %>%
subplot(shareX = TRUE) %>%
layout(title = "Numeric Variable Distributions (scaled)",
yaxis=list(title='Standard Deviation'),
xaxis=list(title='Variable'),
autosize=FALSE,
width=900,
height=500)Specifying width/height in layout() is now deprecated.
Please specify in ggplotly() or plot_ly()Scatterplots
Here we plot all numeric variables against Sales (scaled). This allows us to investigate possible linear relationships between that variable and Sales. As shown below, only ‘Price’ appears to have a linear relationship worth investigating. This took me so long to figure out.
numeric.scatterplots <- htmltools::tagList()
count = 1
for (i in names(scaled.nums[,-1])) {
numeric.scatterplots[[count]] <- plot_ly(scaled.nums, x=scaled.nums[,i], y=scaled.nums$Sales,
colors = 'RdYlGn',
mode = 'markers',
type = 'scatter',
size = scaled.nums$Sales^2,
color = scaled.nums$Sales,
marker = list(line = list(color = 'black',width = 2)),
name=paste(i)) %>%
layout(title = paste(i, "vs Sales (scaled)<br>Size=Sales^2"),
yaxis=list(title='Sales'),
xaxis=list(title=i),
showlegend = FALSE)
count = count + 1
}
numeric.scatterplots`line.width` does not currently support multiple values.`line.width` does not currently support multiple values.`line.width` does not currently support multiple values.`line.width` does not currently support multiple values.`line.width` does not currently support multiple values.`line.width` does not currently support multiple values.`line.width` does not currently support multiple values.`line.width` does not currently support multiple values.`line.width` does not currently support multiple values.`line.width` does not currently support multiple values.`line.width` does not currently support multiple values.`line.width` does not currently support multiple values.`line.width` does not currently support multiple values.`line.width` does not currently support multiple values.By adding naive regression lines to a few scatter plots we can confirm our suspicions:
fit.Pop <- lm(Sales ~ Population, data = scaled.nums)
fit.Age <- lm(Sales ~ Age, data = scaled.nums)
fit.CompPrice <- lm(Sales ~ CompPrice, data = scaled.nums)
fit.Price <- lm(Sales ~ Price, data = scaled.nums)
regression.scatterplots <- htmltools::tagList()
regression.scatterplots[[1]] <- plot_ly(scaled.nums,
x = ~Population,
name = 'Population vs Sales Regression Line') %>%
add_markers(y = ~Sales,
name = 'Population vs Sales Observations') %>%
add_lines(x = ~Population,
y = fitted(fit.Pop)) %>%
layout(title = "Population vs Sales",
yaxis=list(title='Sales',
xaxis=list(title='Population')),
showlegend = FALSE)
regression.scatterplots[[2]] <- plot_ly(scaled.nums,
x = ~Age,
name = 'Age vs Sales Regression Line') %>%
add_markers(y = ~Sales,
name = 'Age vs Sales Observations') %>%
add_lines(x = ~Age,
y = fitted(fit.Age)) %>%
layout(title = "Age vs Sales",
yaxis=list(title='Sales',
xaxis=list(title='Age')),
showlegend = FALSE)
regression.scatterplots[[3]] <- plot_ly(scaled.nums,
x = ~CompPrice,
name = 'CompPrice vs Sales Regression Line') %>%
add_markers(y = ~Sales,
name = 'CompPrice vs Sales Observations') %>%
add_lines(x = ~CompPrice,
y = fitted(fit.CompPrice)) %>%
layout(title = "CompPrice vs Sales",
yaxis=list(title='Sales',
xaxis=list(title='CompPrice')),
showlegend = FALSE)
regression.scatterplots[[4]] <- plot_ly(scaled.nums,
x = ~Price,
name = 'Price vs Sales Regression Line') %>%
add_markers(y = ~Sales,
name = 'Price vs Sales Observations') %>%
add_lines(x = ~Price,
y = fitted(fit.Price)) %>%
layout(title = "Price vs Sales",
yaxis=list(title='Sales',
xaxis=list(title='Price')),
showlegend = FALSE)
regression.scatterplotsLet’s compare the slopes:
scaled.nums %>%
plot_ly(y = ~Sales) %>%
add_lines(x= ~Population, y = fitted(fit.Pop),
name = "fit.Pop slope", line = list(shape = "linear")) %>%
add_lines(x= ~Age, y = fitted(fit.Age),
name = "fit.Age slope", line = list(shape = "linear")) %>%
add_lines(x= ~CompPrice, y = fitted(fit.CompPrice),
name = "fit.CompPrice slope", line = list(shape = "linear")) %>%
add_lines(x= ~Price, y = fitted(fit.Price),
name = "fit.Price slope", line = list(shape = "linear")) %>%
layout(title = "Regression Lines vs Sales (scaled)",
autosize=FALSE,
width=900,
yaxis=list(title='Sales'),
xaxis=list(title='Scaled Numeric Variable'))Specifying width/height in layout() is now deprecated.
Please specify in ggplotly() or plot_ly()Here’s a pretty graphic that doesn’t help me understand anything about the data.
y = scaled.nums$Sales
x = scaled.nums$Price
s <- subplot(
plot_ly(x = x, color = I("black"), type = 'histogram'),
plotly_empty(),
plot_ly(x = x, y = y, type = 'histogram2dcontour', showscale = F),
plot_ly(y = y, color = I("black"), type = 'histogram'),
nrows = 2, heights = c(0.2, 0.8), widths = c(0.8, 0.2),
shareX = TRUE, shareY = TRUE, titleX = FALSE, titleY = FALSE)No trace type specified and no positional attributes specifiedNo trace type specified:
Based on info supplied, a 'scatter' trace seems appropriate.
Read more about this trace type -> https://plot.ly/r/reference/#scatter
No scatter mode specifed:
Setting the mode to markers
Read more about this attribute -> https://plot.ly/r/reference/#scatter-modelayout(s, showlegend = FALSE, autosize=FALSE,
width=700,
height=500,
yaxis=list(title='Sales'),
xaxis=list(title='Price'))Specifying width/height in layout() is now deprecated.
Please specify in ggplotly() or plot_ly()Categorical Plotting
First, let’s create a data frame that we can use:
categorical.by.sales = cbind(Sales = scaled.nums$Sales, cats)
str(categorical.by.sales)'data.frame': 400 obs. of 4 variables:
$ Sales : num 0.7095 1.3185 0.9078 -0.0341 -1.1849 ...
$ ShelveLoc: Factor w/ 3 levels "Bad","Good","Medium": 1 2 3 3 1 1 3 2 3 3 ...
$ Urban : Factor w/ 2 levels "No","Yes": 2 2 2 2 2 1 2 2 1 1 ...
$ US : Factor w/ 2 levels "No","Yes": 2 2 2 2 1 2 1 2 1 2 ...Here we can see all categorical by Sales. We suspected that ‘ShelveLoc’ would be important based on one of the early scatter plots. It seems that this is the case.
categorical.boxplots <- htmltools::tagList()
count = 1
for (i in names(categorical.by.sales[,-1])) {
categorical.boxplots[[count]] <- plot_ly(categorical.by.sales, x=categorical.by.sales[,i], y=categorical.by.sales$Sales,
type = "box",
boxpoints = "all",
jitter = .2,
pointpos = 0,
color =categorical.by.sales[,i],
colors='Set1',
name=paste(i)) %>%
layout(title = paste(i, "vs Sales (scaled)"),
showlegend = TRUE,
yaxis=list(title='Sales Standard Deviation'),
xaxis=list(title=i))
count = count + 1
}
categorical.boxplotsHere’s the same thing, but more musically:
categorical.violins <- htmltools::tagList()
count = 1
for (i in names(categorical.by.sales[,-1])) {
categorical.violins[[count]] <- plot_ly(categorical.by.sales, x=categorical.by.sales[,i], y=categorical.by.sales$Sales,
split = categorical.by.sales[,i],
type = 'violin',
colors='Set1',
name=paste(i),
box = list(visible = TRUE),
meanline = list(visible = TRUE)) %>%
layout(xaxis = list(title = "US"),
yaxis = list(title = "Sales",zeroline = FALSE))
count = count + 1
}
categorical.violinsLinear Regression
First, let’s merge the data set into a single data frame
scaled.merged <- cbind(categorical.by.sales[,-1], scaled.nums)
str(scaled.merged)'data.frame': 400 obs. of 11 variables:
$ ShelveLoc : Factor w/ 3 levels "Bad","Good","Medium": 1 2 3 3 1 1 3 2 3 3 ...
$ Urban : Factor w/ 2 levels "No","Yes": 2 2 2 2 2 1 2 2 1 1 ...
$ US : Factor w/ 2 levels "No","Yes": 2 2 2 2 1 2 1 2 1 2 ...
$ Sales : num 0.7095 1.3185 0.9078 -0.0341 -1.1849 ...
$ CompPrice : num 0.849 -0.911 -0.781 -0.52 1.045 ...
$ Income : num 0.155 -0.738 -1.203 1.12 -0.166 ...
$ Advertising: num 0.656 1.408 0.506 -0.396 -0.547 ...
$ Population : num 0.0757 -0.0328 0.0282 1.3649 0.51 ...
$ Price : num 0.178 -1.385 -1.512 -0.794 0.515 ...
$ Age : num -0.699 0.721 0.35 0.104 -0.946 ...
$ Education : num 1.183 -1.4882 -0.725 0.0382 -0.3434 ...head(nums, 2)tail(nums, 2)head(scaled.merged, 2)tail(scaled.merged, 2)First, let’s look at some things that may give us trouble. Luckily it looks like the only serious correlation is with our dependent variable. We’ll want to watch the ‘Price’ vs ‘CompPrice’ relationship.
res <- cor(scaled.nums)
corrplot(res, type = "upper", order = "hclust",
tl.col = "black", tl.srt = 45)
It appears that residuals are roughly symmetrical around 0. That’s strange. Mostly due to a relatively poor overall fit. Note how close to zero most of the coefficient estimates are.
simple.lm <- lm(Sales~., data=scaled.merged)
simple.summary <- summary(simple.lm)
print(simple.summary)
Call:
lm(formula = Sales ~ ., data = scaled.merged)
Residuals:
Min 1Q Median 3Q Max
-1.01598 -0.24463 0.00748 0.23496 1.20797
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.73292 0.05999 -12.217 < 2e-16 ***
ShelveLocGood 1.71742 0.05422 31.678 < 2e-16 ***
ShelveLocMedium 0.69286 0.04465 15.516 < 2e-16 ***
UrbanYes 0.04351 0.04000 1.088 0.277
USYes -0.06519 0.05306 -1.229 0.220
CompPrice 0.50397 0.02252 22.378 < 2e-16 ***
Income 0.15660 0.01828 8.565 2.58e-16 ***
Advertising 0.28987 0.02619 11.066 < 2e-16 ***
Population 0.01085 0.01933 0.561 0.575
Price -0.79946 0.02239 -35.700 < 2e-16 ***
Age -0.26413 0.01825 -14.472 < 2e-16 ***
Education -0.01958 0.01830 -1.070 0.285
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.3608 on 388 degrees of freedom
Multiple R-squared: 0.8734, Adjusted R-squared: 0.8698
F-statistic: 243.4 on 11 and 388 DF, p-value: < 2.2e-16Linear Models and Subsets
Let’s do the same thing, but control the subsets using leaps
regfit.full=regsubsets(Sales~., data=scaled.merged, nvmax=5)
reg.summary=summary(regfit.full)
print(reg.summary)Subset selection object
Call: regsubsets.formula(Sales ~ ., data = scaled.merged, nvmax = 5)
11 Variables (and intercept)
Forced in Forced out
ShelveLocGood FALSE FALSE
ShelveLocMedium FALSE FALSE
UrbanYes FALSE FALSE
USYes FALSE FALSE
CompPrice FALSE FALSE
Income FALSE FALSE
Advertising FALSE FALSE
Population FALSE FALSE
Price FALSE FALSE
Age FALSE FALSE
Education FALSE FALSE
1 subsets of each size up to 5
Selection Algorithm: exhaustive
ShelveLocGood ShelveLocMedium UrbanYes USYes CompPrice Income Advertising Population Price Age Education
1 ( 1 ) "*" " " " " " " " " " " " " " " " " " " " "
2 ( 1 ) "*" " " " " " " " " " " " " " " "*" " " " "
3 ( 1 ) "*" " " " " " " "*" " " " " " " "*" " " " "
4 ( 1 ) "*" " " " " " " "*" " " "*" " " "*" " " " "
5 ( 1 ) "*" "*" " " " " "*" " " "*" " " "*" " " " " We’ll just take code straight from the example on Canvas…
par(mfrow=c(2,2))
plot(reg.summary$rss,xlab="Number of Variables",ylab="RSS",type="l")
plot(reg.summary$adjr2,xlab="Number of Variables",ylab="Adjusted RSq",type="l")plot(reg.summary$cp,xlab="Number of Variables",ylab="Cp",type='l')
plot(reg.summary$bic,xlab="Number of Variables",ylab="BIC",type='l')
plot(regfit.full,scale="r2")
plot(regfit.full,scale="adjr2")
plot(regfit.full,scale="Cp")
plot(regfit.full,scale="bic")
Interaction Terms
Here we define a new model with some interaction terms: a. Income and Advertising b. Income and CompPrice c. Price and Age
interaction.lm <- lm(Sales~. + Income*Advertising + Income*CompPrice + Price*Age, data=scaled.merged)
interaction.summary <- summary(interaction.lm)
print(interaction.summary)
Call:
lm(formula = Sales ~ . + Income * Advertising + Income * CompPrice +
Price * Age, data = scaled.merged)
Residuals:
Min 1Q Median 3Q Max
-1.04967 -0.23955 -0.00936 0.24591 1.19774
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.730051 0.059236 -12.324 < 2e-16 ***
ShelveLocGood 1.714324 0.053519 32.032 < 2e-16 ***
ShelveLocMedium 0.680563 0.044177 15.405 < 2e-16 ***
UrbanYes 0.045257 0.039380 1.149 0.25117
USYes -0.069622 0.052329 -1.330 0.18415
CompPrice 0.507567 0.022131 22.935 < 2e-16 ***
Income 0.152164 0.018025 8.442 6.43e-16 ***
Advertising 0.289455 0.025756 11.238 < 2e-16 ***
Population 0.007224 0.018985 0.381 0.70377
Price -0.797242 0.022003 -36.233 < 2e-16 ***
Age -0.260783 0.017978 -14.505 < 2e-16 ***
Education -0.024248 0.018063 -1.342 0.18027
Income:Advertising 0.046378 0.018170 2.552 0.01108 *
CompPrice:Income -0.059184 0.018911 -3.130 0.00188 **
Price:Age 0.013171 0.017912 0.735 0.46259
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.3538 on 385 degrees of freedom
Multiple R-squared: 0.8792, Adjusted R-squared: 0.8748
F-statistic: 200.1 on 14 and 385 DF, p-value: < 2.2e-16interaction.lm.subsets <- regsubsets(Sales~. + Income*Advertising + Income*CompPrice + Price*Age,
data=scaled.merged, nvmax=5)
interaction.subsets.summary <- summary(interaction.lm.subsets)
print(interaction.subsets.summary)Subset selection object
Call: regsubsets.formula(Sales ~ . + Income * Advertising + Income *
CompPrice + Price * Age, data = scaled.merged, nvmax = 5)
14 Variables (and intercept)
Forced in Forced out
ShelveLocGood FALSE FALSE
ShelveLocMedium FALSE FALSE
UrbanYes FALSE FALSE
USYes FALSE FALSE
CompPrice FALSE FALSE
Income FALSE FALSE
Advertising FALSE FALSE
Population FALSE FALSE
Price FALSE FALSE
Age FALSE FALSE
Education FALSE FALSE
Income:Advertising FALSE FALSE
CompPrice:Income FALSE FALSE
Price:Age FALSE FALSE
1 subsets of each size up to 5
Selection Algorithm: exhaustive
ShelveLocGood ShelveLocMedium UrbanYes USYes CompPrice Income Advertising Population Price Age Education
1 ( 1 ) "*" " " " " " " " " " " " " " " " " " " " "
2 ( 1 ) "*" " " " " " " " " " " " " " " "*" " " " "
3 ( 1 ) "*" " " " " " " "*" " " " " " " "*" " " " "
4 ( 1 ) "*" " " " " " " "*" " " "*" " " "*" " " " "
5 ( 1 ) "*" "*" " " " " "*" " " "*" " " "*" " " " "
Income:Advertising CompPrice:Income Price:Age
1 ( 1 ) " " " " " "
2 ( 1 ) " " " " " "
3 ( 1 ) " " " " " "
4 ( 1 ) " " " " " "
5 ( 1 ) " " " " " " Variable Significance
Below we print the coefficients for the 5th model using the default model selection criteria. All coefficients are relatively small, as we would expect from the EDA above. This pretty much confirms what I would have guessed by looking at the data against sales. We still want to watch out for confounding between ‘Price’ and ‘CompPrice.’
coef(interaction.lm.subsets, 5) (Intercept) ShelveLocGood ShelveLocMedium CompPrice Advertising Price
-0.6995348 1.6746198 0.6277225 0.5090177 0.2832405 -0.7846476 Second Interaction Model
First, drop columns unneeded from analysis:
scaled.merged.slim <- scaled.merged[ , -which(names(scaled.merged) %in% c("US","Urban"))]A few hyper parameters we’d like to be consistent for all models
nvmax <- 3Forward Selection:
interaction.subset.fwd <- regsubsets(Sales~. + Income*Advertising + Income*CompPrice + Income*Age,
data=scaled.merged.slim,
nvmax = nvmax,
method="forward")
fwd.subset.summary <- summary(interaction.subset.fwd)
coef(interaction.subset.fwd, 1:nvmax)[[1]]
(Intercept) ShelveLocGood
-0.259671 1.221981
[[2]]
(Intercept) ShelveLocGood Price
-0.2708256 1.2744733 -0.4688868
[[3]]
(Intercept) ShelveLocGood CompPrice Price
-0.2709362 1.2749938 0.4932455 -0.7573701 Backward Selection:
This is really strange. I can’t seem to find any documentation about this, but it appears that this model is actually ‘forward.’
interaction.subset.bk <- regsubsets(Sales~. + Income*Advertising + Income*CompPrice + Income*Age,
data=scaled.merged.slim,
nvmax = nvmax,
method="backward")
bk.subset.summary <- summary(interaction.subset.bk)
coef(interaction.subset.bk, 1:nvmax)[[1]]
(Intercept) ShelveLocGood
-0.259671 1.221981
[[2]]
(Intercept) ShelveLocGood Price
-0.2708256 1.2744733 -0.4688868
[[3]]
(Intercept) ShelveLocGood CompPrice Price
-0.2709362 1.2749938 0.4932455 -0.7573701 Exhasutive
interaction.subset.ex <- regsubsets(Sales~. + Income*Advertising + Income*CompPrice + Income*Age,
data=scaled.merged.slim,
nvmax = nvmax,
method="exhaustive")
ex.subset.summary <- summary(interaction.subset.ex)
coef(interaction.subset.ex, 1:nvmax)[[1]]
(Intercept) ShelveLocGood
-0.259671 1.221981
[[2]]
(Intercept) ShelveLocGood Price
-0.2708256 1.2744733 -0.4688868
[[3]]
(Intercept) ShelveLocGood CompPrice Price
-0.2709362 1.2749938 0.4932455 -0.7573701 This is a list that may come in handy.
model.list = list(list("Forward", interaction.subset.fwd, fwd.subset.summary),
list("Backward", interaction.subset.bk, bk.subset.summary),
list("Exhaustive", interaction.subset.ex, ex.subset.summary))Evaluation Metric Plotting
It is interesting to see that each model selected the same variables, in the same order.
par(mfrow=c(2,2))
plot(fwd.subset.summary$rss,xlab="Number of Variables (forward)",ylab="RSS",type="l")
plot(fwd.subset.summary$adjr2,xlab="Number of Variables (forward)",ylab="Adjusted RSq",type="l")plot(fwd.subset.summary$cp,xlab="Number of Variables (forward)",ylab="Cp",type='l')
plot(fwd.subset.summary$bic,xlab="Number of Variables (forward)",ylab="BIC",type='l')
par(mfrow=c(2,2))
plot(bk.subset.summary$rss,xlab="Number of Variables (backward)",ylab="RSS",type="l")
plot(bk.subset.summary$adjr2,xlab="Number of Variables (backward)",ylab="Adjusted RSq",type="l")plot(bk.subset.summary$cp,xlab="Number of Variables (backward)",ylab="Cp",type='l')
plot(bk.subset.summary$bic,xlab="Number of Variables (backward)",ylab="BIC",type='l')
par(mfrow=c(2,2))
plot(ex.subset.summary$rss,xlab="Number of Variables (exhaustive)",ylab="RSS",type="l")
plot(ex.subset.summary$adjr2,xlab="Number of Variables (exhaustive)",ylab="Adjusted RSq",type="l")plot(ex.subset.summary$cp,xlab="Number of Variables (exhaustive)",ylab="Cp",type='l')
plot(ex.subset.summary$bic,xlab="Number of Variables (exhaustive)",ylab="BIC",type='l')
Model Equations
Here we print the final equations for each model. Not, they are all the same.
for (mod.obj in model.list) {
mod.name <- mod.obj[[1]]
best.bic <- min(mod.obj[[3]]$bic)
mod.num <- which.min(mod.obj[[3]]$bic)
mod.cc <- coef(mod.obj[[2]], mod.num)
mod.equation.format <- paste("Y =", paste(round(mod.cc[1],2),
paste(round(mod.cc[-1],2),
names(mod.cc[-1]),
sep=" * ", collapse=" + "),
sep=" + "), "+ e")
print(paste("Model Selection Method: ",mod.name))
print(paste("Min BIC:", best.bic))
print(paste("Model Number: ", mod.num))
print(paste("Model Equation: ", mod.equation.format))
print("")
}[1] "Model Selection Method: Forward"
[1] "Min BIC: -373.710213587368"
[1] "Model Number: 3"
[1] "Model Equation: Y = -0.27 + 1.27 * ShelveLocGood + 0.49 * CompPrice + -0.76 * Price + e"
[1] ""
[1] "Model Selection Method: Backward"
[1] "Min BIC: -373.710213587368"
[1] "Model Number: 3"
[1] "Model Equation: Y = -0.27 + 1.27 * ShelveLocGood + 0.49 * CompPrice + -0.76 * Price + e"
[1] ""
[1] "Model Selection Method: Exhaustive"
[1] "Min BIC: -373.710213587368"
[1] "Model Number: 3"
[1] "Model Equation: Y = -0.27 + 1.27 * ShelveLocGood + 0.49 * CompPrice + -0.76 * Price + e"
[1] ""---
title: "Carseats R Notebook"
output: html_notebook
---

# Introduction
Here is my analysis of `data/Carseats_org.csv`. 

## Configuration

```{r}
library(leaps)
library(stringr)
library(caret)
library(ggplot2)
library(DataExplorer)
library(dplyr)
library(ggExtra)
library(RColorBrewer)
library(plotly)
library(corrplot)
library(htmltools)
library(MASS)
```

## System Information
Due to the large number of libraries in use I have provided system information.

```{r}
sessionInfo()
sapply(c('repr', 'IRdisplay', 'IRkernel'), function(p) paste(packageVersion(p)))
```

# Data
I load the data into `r`, and drop the "ID" column. 

```{r}
carseats <- read.csv("data/Carseats_org.csv", header = T, stringsAsFactors = T)

drops <- c("X")
carseats <- carseats[ , !(names(carseats) %in% drops)]
head(carseats, 10)
```

Here I create two new data frames to manage numeric and categorical data.

```{r}
# get vectors of continuous and categorical cols
nums <- dplyr::select_if(carseats, is.numeric)
cats <- dplyr::select_if(carseats, is.factor)

nums[sample(nrow(nums), 10), ]

cats[sample(nrow(cats), 10), ]
```

Let's get some quick summaries of each:

```{r}
print('Numeric Summaries')
summary(nums)
print('Categorical Summaries')
summary(cats)
```

```{r}
str(nums)
str(cats)
```


## Data Dimensionality
This command is to inspect the different data types in the data. 

```{r}
str(carseats)
print("")
print(paste('Number of Columns:', ncol(carseats)))
print(paste('Number of Numeric Columns:', ncol(nums)))
print(paste('Number of Categorical Columns:', ncol(cats)))
```

```{r}
dim(carseats)
dim(nums)
dim(cats)
```


Here's a quick way to examine general properties of the data:

```{r}
DataExplorer::introduce(data=carseats)
```

Finally, I want to look at the first and last rows of the data set. Just to be safe:

```{r}
head(carseats, 2)
tail(carseats, 2)

head(nums, 2)
tail(nums, 2)

head(cats, 2)
tail(cats, 2)
```



# Numeric Plotting
I start out with a few general scatter plots.

```{r}
plot_ly(data=carseats, 
        x=~Age, 
        y=~Sales, 
        mode = 'markers', 
        type = 'scatter', 
        color=~ShelveLoc) %>%
            layout(title = "Age, Shelf Location, and Sales Scatter Plot", width=900) 
```

This plot below shows good separation and a weak linear trend. These variables are worth investigating.

```{r}
plot_ly(data=carseats, 
        x=~Price, 
        y=~Sales, 
        mode = 'markers', 
        type = 'scatter', 
        color=~ShelveLoc) %>%
            layout(title = "Price, Shelf Location, and Sales Scatter Plot", width=900)
```

Here we inspect the density of the 'Price vs Sales' relationship:

```{r}
plot_ly(data=carseats, 
        x=~Price, 
        y=~Sales, 
        mode = 'markers', 
        size = ~Price,
        type = 'scatter',
        colors = "Dark2",
        alpha = .6) %>%
            layout(title = "Price, US, and Sales Scatter Plot", width=900) 
```

# Normalization
I choose to normalize the numeric data in order to be able to plot each variable on the same scale. This will allow me to investigate the variation of each predictor relative to Sales.

```{r}
preObj <- preProcess(nums, method=c("center", "scale"))
scaled.nums <- predict(preObj, nums)

head(scaled.nums, 2)
tail(scaled.nums, 2)
```

```{r}
str(scaled.nums)
print("")
summary(scaled.nums)
```

## Distributions
Here are scaled distributions (histograms and density plots) for each numeric variable, including Sales. The variables relating to money ($) tend to be approximately normal. Many other variables tend to be approximately uniform, which does not bode well for their predictive power.

```{r}
scaled.nums %>%
    tidyr::gather() %>% 
        ggplot(aes(x=value,y=..density..))+

            ggtitle('Distributions of Continous Variables (scaled)') +

            facet_wrap(~ key, scales = "free") +
            geom_histogram(fill=I("orange"), col=I("black"), bins = 50) +

            facet_wrap(~ key, scales = "free") +
            geom_density(color="blue", fill='light blue', alpha = 0.4)
```

Here we plot all numeric variables against their distributions. This is just another way to examine the information shown above.

```{r}
scaled.nums %>%
    tidyr::gather() %>% 
        plot_ly(x=~key, y=~value,
                type = "box", 
                boxpoints = "all", 
                jitter = 0.4,
                pointpos = 0,
                color = ~key,
                colors = "Dark2") %>%
                      subplot(shareX = TRUE)  %>%
                            layout(title = "Numeric Variable Distributions (scaled)", 
                                  yaxis=list(title='Standard Deviation'),
                                  xaxis=list(title='Variable'),
                                  autosize=FALSE,
                                  width=900,
                                  height=500)
```

## Scatterplots

Here we plot all numeric variables against Sales (scaled). This allows us to investigate possible linear relationships between that variable and Sales. As shown below, only 'Price' appears to have a linear relationship worth investigating. This took me so long to figure out. 

```{r}

numeric.scatterplots <- htmltools::tagList()
count = 1

for (i in names(scaled.nums[,-1])) {
  
  numeric.scatterplots[[count]] <- plot_ly(scaled.nums, x=scaled.nums[,i], y=scaled.nums$Sales,
                    colors = 'RdYlGn',
                    mode = 'markers',
                    type = 'scatter',
                    size = scaled.nums$Sales^2,
                    color = scaled.nums$Sales,
                    marker = list(line = list(color = 'black',width = 2)),
                    name=paste(i)) %>%
          layout(title = paste(i, "vs Sales (scaled)<br>Size=Sales^2"),
                               yaxis=list(title='Sales'),
                               xaxis=list(title=i),
                               showlegend = FALSE)
  
  count = count + 1
  
}

numeric.scatterplots

```

By adding naive regression lines to a few scatter plots we can confirm our suspicions:

```{r}
fit.Pop <- lm(Sales ~ Population, data = scaled.nums)
fit.Age <- lm(Sales ~ Age, data = scaled.nums)
fit.CompPrice <- lm(Sales ~ CompPrice, data = scaled.nums)
fit.Price <- lm(Sales ~ Price, data = scaled.nums)

regression.scatterplots <- htmltools::tagList()

regression.scatterplots[[1]] <-  plot_ly(scaled.nums, 
          x = ~Population,
          name = 'Population vs Sales Regression Line') %>% 
              add_markers(y = ~Sales,
                    name = 'Population vs Sales Observations') %>% 
                            add_lines(x = ~Population, 
                                  y = fitted(fit.Pop)) %>%
                                        layout(title = "Population vs Sales",
                                               yaxis=list(title='Sales',
                                               xaxis=list(title='Population')),
                                               showlegend = FALSE)
                                              
           

regression.scatterplots[[2]] <-  plot_ly(scaled.nums, 
          x = ~Age,
          name = 'Age vs Sales Regression Line') %>% 
              add_markers(y = ~Sales,
                    name = 'Age vs Sales Observations') %>% 
                            add_lines(x = ~Age, 
                                  y = fitted(fit.Age)) %>%
                                        layout(title = "Age vs Sales",
                                               yaxis=list(title='Sales',
                                               xaxis=list(title='Age')),
                                               showlegend = FALSE)

regression.scatterplots[[3]] <-  plot_ly(scaled.nums, 
          x = ~CompPrice,
          name = 'CompPrice vs Sales Regression Line') %>% 
              add_markers(y = ~Sales,
                    name = 'CompPrice vs Sales Observations') %>% 
                            add_lines(x = ~CompPrice, 
                                  y = fitted(fit.CompPrice)) %>%
                                        layout(title = "CompPrice vs Sales",
                                               yaxis=list(title='Sales',
                                               xaxis=list(title='CompPrice')),
                                               showlegend = FALSE)

regression.scatterplots[[4]] <-  plot_ly(scaled.nums, 
          x = ~Price,
          name = 'Price vs Sales Regression Line') %>% 
              add_markers(y = ~Sales,
                    name = 'Price vs Sales Observations') %>% 
                            add_lines(x = ~Price, 
                                  y = fitted(fit.Price)) %>%
                                        layout(title = "Price vs Sales",
                                               yaxis=list(title='Sales',
                                               xaxis=list(title='Price')),
                                               showlegend = FALSE)


regression.scatterplots
```

Let's compare the slopes:

```{r}
scaled.nums %>%
    plot_ly(y = ~Sales) %>%
      add_lines(x= ~Population, y = fitted(fit.Pop), 
                name = "fit.Pop slope", line = list(shape = "linear")) %>%
      add_lines(x= ~Age, y = fitted(fit.Age), 
                name = "fit.Age slope", line = list(shape = "linear")) %>%
      add_lines(x= ~CompPrice, y = fitted(fit.CompPrice), 
                name = "fit.CompPrice slope", line = list(shape = "linear")) %>%
      add_lines(x= ~Price, y = fitted(fit.Price), 
                name = "fit.Price slope", line = list(shape = "linear")) %>%
            
    layout(title = "Regression Lines vs Sales (scaled)",
           autosize=FALSE,
           width=900,
           yaxis=list(title='Sales'),
           xaxis=list(title='Scaled Numeric Variable'))
```

Here's a pretty graphic that doesn't help me understand anything about the data.

```{r}
y = scaled.nums$Sales
x = scaled.nums$Price

s <- subplot(
  plot_ly(x = x, color = I("black"), type = 'histogram'), 
  plotly_empty(), 
  plot_ly(x = x, y = y, type = 'histogram2dcontour', showscale = F), 
  plot_ly(y = y, color = I("black"), type = 'histogram'),
  nrows = 2, heights = c(0.2, 0.8), widths = c(0.8, 0.2),
  shareX = TRUE, shareY = TRUE, titleX = FALSE, titleY = FALSE)

layout(s, showlegend = FALSE, autosize=FALSE,
           width=700,
           height=500, 
           yaxis=list(title='Sales'),
           xaxis=list(title='Price'))
```

# Categorical Plotting
First, let's create a data frame that we can use:
```{r}
categorical.by.sales = cbind(Sales = scaled.nums$Sales, cats)
str(categorical.by.sales)
```

Here we can see all categorical by Sales. We suspected that 'ShelveLoc' would be important based on one of the early scatter plots. It seems that this is the case.

```{r}

categorical.boxplots <- htmltools::tagList()
count = 1

for (i in names(categorical.by.sales[,-1])) {
  
  categorical.boxplots[[count]] <- plot_ly(categorical.by.sales, x=categorical.by.sales[,i], y=categorical.by.sales$Sales,
                        type = "box", 
                        boxpoints = "all",
                        jitter = .2,
                        pointpos = 0,
                        color =categorical.by.sales[,i],
                        colors='Set1', 
                        name=paste(i)) %>%
                            layout(title = paste(i, "vs Sales (scaled)"),
                                  showlegend = TRUE,
                                  yaxis=list(title='Sales Standard Deviation'),
                                  xaxis=list(title=i))
  
  count = count + 1
  
}

categorical.boxplots
```

Here's the same thing, but more musically:

```{r}

categorical.violins <- htmltools::tagList()
count = 1

for (i in names(categorical.by.sales[,-1])) {
  
  categorical.violins[[count]] <- plot_ly(categorical.by.sales, x=categorical.by.sales[,i], y=categorical.by.sales$Sales,
                        split = categorical.by.sales[,i],
                        type = 'violin',
                        colors='Set1', 
                        name=paste(i),
                        box = list(visible = TRUE),
                        meanline = list(visible = TRUE)) %>% 
                            layout(xaxis = list(title = "US"),
                                yaxis = list(title = "Sales",zeroline = FALSE))

  
  count = count + 1
  
}

categorical.violins
```

# Linear Regression

First, let's merge the data set into a single data frame
```{r}

scaled.merged <- cbind(categorical.by.sales[,-1], scaled.nums)
str(scaled.merged)
```

```{r}
head(nums, 2)
tail(nums, 2)

head(scaled.merged, 2)
tail(scaled.merged, 2)
```


First, let's look at some things that may give us trouble. Luckily it looks like the only serious correlation is with our dependent variable. We'll want to watch the 'Price' vs 'CompPrice' relationship.

```{r}
res <- cor(scaled.nums)

corrplot(res, type = "upper", order = "hclust", 
         tl.col = "black", tl.srt = 45)
```

It appears that residuals are roughly symmetrical around 0. That's strange. Mostly due to a relatively poor overall fit. Note how close to zero most of the coefficient estimates are.

```{r}
simple.lm <- lm(Sales~., data=scaled.merged)
simple.summary <- summary(simple.lm)

print(simple.summary)
```

## Linear Models and Subsets

Let's do the same thing, but control the subsets using `leaps`

```{r}
regfit.full=regsubsets(Sales~., data=scaled.merged, nvmax=5)
reg.summary=summary(regfit.full)

print(reg.summary)
```

We'll just take code straight from the example on Canvas...

```{r}
par(mfrow=c(2,2))
plot(reg.summary$rss,xlab="Number of Variables",ylab="RSS",type="l")
plot(reg.summary$adjr2,xlab="Number of Variables",ylab="Adjusted RSq",type="l")
plot(reg.summary$cp,xlab="Number of Variables",ylab="Cp",type='l')
plot(reg.summary$bic,xlab="Number of Variables",ylab="BIC",type='l')
```

```{r}
plot(regfit.full,scale="r2")
plot(regfit.full,scale="adjr2")
plot(regfit.full,scale="Cp")
plot(regfit.full,scale="bic")
```


# Interaction Terms

Here we define a new model with some interaction terms: 
    a.  Income and Advertising
    b.  Income and CompPrice
    c.   Price and Age


```{r}
interaction.lm <- lm(Sales~. + Income*Advertising + Income*CompPrice + Price*Age, data=scaled.merged)
interaction.summary <- summary(interaction.lm)

print(interaction.summary)
```

```{r}
interaction.lm.subsets <- regsubsets(Sales~. + Income*Advertising + Income*CompPrice + Price*Age, 
                                     data=scaled.merged, nvmax=5)

interaction.subsets.summary <- summary(interaction.lm.subsets)

print(interaction.subsets.summary)
```


## Variable Significance
Below we print the coefficients for the 5th model using the default model selection criteria. All coefficients are relatively small, as we would expect from the EDA above. This pretty much confirms what I would have guessed by looking at the data against sales. We still want to watch out for confounding between 'Price' and 'CompPrice.'


```{r}
coef(interaction.lm.subsets, 5)
```

## Second Interaction Model

First, drop columns unneeded from analysis:

```{r}
scaled.merged.slim <- scaled.merged[ , -which(names(scaled.merged) %in% c("US","Urban"))]
```


A few hyper parameters we'd like to be consistent for all models

```{r}
nvmax <- 3
```

## Forward Selection:

```{r}
interaction.subset.fwd <- regsubsets(Sales~. + Income*Advertising + Income*CompPrice + Income*Age,
                                     data=scaled.merged.slim, 
                                     nvmax = nvmax,
                                     method="forward")

fwd.subset.summary <- summary(interaction.subset.fwd)

coef(interaction.subset.fwd, 1:nvmax)
```

## Backward Selection:

This is really strange. I can't seem to find any documentation about this, but it appears that this model is actually 'forward.'

```{r}
interaction.subset.bk <- regsubsets(Sales~. + Income*Advertising + Income*CompPrice + Income*Age,
                                     data=scaled.merged.slim, 
                                     nvmax = nvmax,
                                     method="backward")

bk.subset.summary <- summary(interaction.subset.bk)

coef(interaction.subset.bk, 1:nvmax)
```

## Exhasutive

```{r}
interaction.subset.ex <- regsubsets(Sales~. + Income*Advertising + Income*CompPrice + Income*Age,
                                     data=scaled.merged.slim, 
                                     nvmax = nvmax,
                                     method="exhaustive")

ex.subset.summary <- summary(interaction.subset.ex)
coef(interaction.subset.ex, 1:nvmax)
```

This is a list that may come in handy.

```{r}
model.list = list(list("Forward", interaction.subset.fwd, fwd.subset.summary), 
                  list("Backward", interaction.subset.bk, bk.subset.summary), 
                  list("Exhaustive", interaction.subset.ex, ex.subset.summary))
```

# Evaluation Metric Plotting

It is interesting to see that each model selected the same variables, in the same order.

```{r}
par(mfrow=c(2,2))
plot(fwd.subset.summary$rss,xlab="Number of Variables (forward)",ylab="RSS",type="l")
plot(fwd.subset.summary$adjr2,xlab="Number of Variables (forward)",ylab="Adjusted RSq",type="l")
plot(fwd.subset.summary$cp,xlab="Number of Variables (forward)",ylab="Cp",type='l')
plot(fwd.subset.summary$bic,xlab="Number of Variables (forward)",ylab="BIC",type='l')
```

```{r}
par(mfrow=c(2,2))
plot(bk.subset.summary$rss,xlab="Number of Variables (backward)",ylab="RSS",type="l")
plot(bk.subset.summary$adjr2,xlab="Number of Variables (backward)",ylab="Adjusted RSq",type="l")
plot(bk.subset.summary$cp,xlab="Number of Variables (backward)",ylab="Cp",type='l')
plot(bk.subset.summary$bic,xlab="Number of Variables (backward)",ylab="BIC",type='l')
```

```{r}
par(mfrow=c(2,2))
plot(ex.subset.summary$rss,xlab="Number of Variables (exhaustive)",ylab="RSS",type="l")
plot(ex.subset.summary$adjr2,xlab="Number of Variables (exhaustive)",ylab="Adjusted RSq",type="l")
plot(ex.subset.summary$cp,xlab="Number of Variables (exhaustive)",ylab="Cp",type='l')
plot(ex.subset.summary$bic,xlab="Number of Variables (exhaustive)",ylab="BIC",type='l')
```

# Model Equations

Here we print the final equations for each model. Not, they are all the same.

```{r}

for (mod.obj in model.list) {
  mod.name <- mod.obj[[1]]
  best.bic <- min(mod.obj[[3]]$bic)
  mod.num <- which.min(mod.obj[[3]]$bic)
  mod.cc <- coef(mod.obj[[2]], mod.num)
  
  mod.equation.format <- paste("Y =", paste(round(mod.cc[1],2), 
                      paste(round(mod.cc[-1],2), 
                      names(mod.cc[-1]), 
                      sep=" * ", collapse=" + "), 
                      sep=" + "), "+ e")
  
  print(paste("Model Selection Method: ",mod.name))
  print(paste("Min BIC:", best.bic))
  print(paste("Model Number: ", mod.num))
  print(paste("Model Equation: ", mod.equation.format))
  print("")
  
}
```




